The invention relates to an X-ray tube which comprises an anode member provided with a cylindrical cavity which can be connected to a cooling medium flow. An X-ray tube of this kind is known from the publication "Leitfaden der medizinischen Rotgentechnik" by van der Plaats,1961, FIG. 21. This tube is an X-ray tube comprising a stationary anode. The stationary anode is provided with a cavity which is penetrated by a cooling medium supply duct. The cooling medium flows through the duct to the end face of the cavity on which the stationary anode is mounted, and subsequently flows back along the cooling medium duct in the cavity. Of interest is commonly owned copending application entitled "Rotary-Anode X-ray Tube Comprising A Sleeve Bearing, Notably A Helical-Groove Bearing", Ser. No. 07/459,914, filed Jan. 2, 1990 in the name of AXEL VETTER.